Classification of Higher Dimensional Algebraic Varieties

• Main Authors: Hacon, Christopher D. (Author), Kovc̀s, Sǹdor. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Basel : Birkhũser Basel, 2010.
• Series: Oberwolfach Seminars ; 41
• Subjects: Mathematics.; Geometry, algebraic.; Algebraic Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-0346-0290-7

This book focuses on recent advances in the classification of complex projective varieties. It is divided into two parts. The first part gives a detailed account of recent results in the minimal model program. In particular, it contains a complete proof of the theorems on the existence of flips, on...

Table of Contents:

• I Basics
• 1 Introduction
• 2 Preliminaries
• 3 Singularities
• 3 Canonical singularities
• II Recent advances in the MMP
• 4 Introduction
• 5 The main result
• 6 Multiplier ideal sheaves
• 7 Finite generation of the restricted algebra
• 7 Rationality of the restricted algebra
• 8 Log terminal models
• 9 Non-vanishing
• 10 Finiteness of log terminal models
• 11 Solutions and hints to some of the exercises
• III Compact moduli spaces
• 12 Moduli problems
• 13 Hilbert schemes
• 14 The construction of the moduli space
• 15 Families and moduli functors
• 16 Subvarieties of moduli spaces
• IV Solutions and hints to some of the exercises.